Sir can you answer the following question?

Substitute y = tan x

dy/dx = sec² x

dy = sec² x dx

f(x) = (sec² x sec² x)/tan x

= (1 + tan² x)(sec² x)/tan x

Hence f(x) dx = (1 + tan² x)(sec² x)dx/tan x

f(x) dx = (1 + y²)dy/y^1/2 = f(y)dy

(y^-1/2 + y^2-1/2)dy = (y^-1/2 + y^3/2)dy

= 2y^1/2 + 2y^5/2/5

= 2tan x (5 + tan² x)/5

Regards,

Team,

TopperLearning.